• Corpus ID: 249063135

# An Asymptotic $\left(\frac{4}{3}+\varepsilon\right)$-Approximation for the 2-Dimensional Vector Bin Packing Problem

@inproceedings{Kulik2022AnA,
title={An Asymptotic \$\left(\frac\{4\}\{3\}+\varepsilon\right)\$-Approximation for the 2-Dimensional Vector Bin Packing Problem},
author={Ariel Kulik and Matthias Mnich and Hadas Shachnai},
year={2022}
}
• Published 25 May 2022
• Mathematics, Computer Science
We study the 2-Dimensional Vector Bin Packing Problem (2VBP), a generalization of classic Bin Packing that is widely applicable in resource allocation and scheduling. In 2VBP we are given a set of items, where each item is associated with a two-dimensional volume vector. The objective is to partition the items into a minimal number of subsets (bins), such that the total volume of items in each subset is at most 1 in each dimension. We give an asymptotic (cid:0) -approximation for the problem…

## References

SHOWING 1-10 OF 33 REFERENCES

### Improved Approximation for Vector Bin Packing

• Computer Science
SODA
• 2016
This work studies the d-dimensional vector bin packing problem, a well-studied generalization of bin packing arising in resource allocation and scheduling problems, using multi-objective multi-budget matching based techniques and expanding the Round & Approx framework to go beyond rounding-based algorithms.

### Bin packing can be solved within 1 + ε in linear time

• Mathematics
• 1981
For any listL ofn numbers in (0, 1) letL* denote the minimum number of unit capacity bins needed to pack the elements ofL. We prove that, for every positive ε, there exists anO(n)-time algorithmS

### The ellipsoid method and its consequences in combinatorial optimization

• Mathematics, Computer Science
Comb.
• 1981
The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.

### A New Approximation Method for Set Covering Problems, with Applications to Multidimensional Bin Packing

• Computer Science, Mathematics
SIAM J. Comput.
• 2009
In this paper we introduce a new general approximation method for set covering problems, based on the combination of randomized rounding of the (near-) optimal solution of the linear programming (LP)

### Multi-budgeted matchings and matroid intersection via dependent rounding

• Mathematics, Computer Science
SODA '11
• 2011
It is shown that for any fixed Δ > 0, a given point x can be rounded to a random solution R such that E[1R] = (1 − Δ)x and any linear function of x satisfies dimension-free Chernoff-Hoeffding concentration bounds.

### There is no APTAS for 2-dimensional vector bin packing: Revisited

It is NP-hard to get an asymptotic approximation ratio better than 600 599, and a revised proof is given using some additional ideas from [2].

### Almost Optimal Inapproximability of Multidimensional Packing Problems

• Sai Sandeep
• Computer Science
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
• 2022
No hardness results that grow with $d were known for Vector Scheduling and Vector Bin Covering when d is part of the input and for Vector Bin Packing when$d\$ is a fixed constant.

### Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping

• Computer Science, Mathematics
ESA
• 2021
A unified algorithm is presented that yields efficient approximations for a wide class of submodular and modular optimization problems involving multiple knapsack constraints, and the robustness of the algorithm is achieved by applying a novel fractional variant of the classical linear grouping technique.

### Autonomic Cloud Placement of Mixed Workload: An Adaptive Bin Packing Algorithm

• Computer Science
2019 IEEE International Conference on Autonomic Computing (ICAC)
• 2019
A novel, autonomic, Adaptive Bin Packing (ABP) algorithm which attempts to equalize measures of variability in the demand and the allocated resources in the cloud, without the need to set any configuration, is introduced.